If $g$ is a regular (not necessarily holomorphic) function, $g:\mathbb{C}\to\mathbb{C}$, is there a way to find a complex function $f$ such that $$ \partial_{\bar{z}}f=g\quad\text{in }\mathbb{C} $$ where $\partial_{\bar{z}}=\partial_x+i\partial_y$? I suspect that the only way is to transform it into a system of first order real differential equations but maybe there is a more clever way I don't know about. Any help is very appreciated.
2026-03-30 05:32:21.1774848741
Is there a way to solve $\partial_{\bar{z}}f=g$
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